Minimum Linear Arrangement of Incomplete Hypercubes

Miller, Mirka; Rajan, R. Sundara; Parthiban, N.; Rajasingh, Indra

doi:10.1093/comjnl/bxu031

Cited by 24 publications

(6 citation statements)

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“…Lemma 1.1. [27] Let f : G → H be an embedding with |V (G)| = |V (H)|. Let S ⊆ E(H) be such that E(H) \ S has exactly two subgraphs H 1 and H 2 , and let…”

Section: E=xy∈e(h)mentioning

confidence: 99%

Embedding complete multi-partite graphs into Cartesian product of paths and cycles

Rajan

Shantrinal

Rajalaxmi

et al. 2021

EJGTA

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Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the wirelength. In this manuscript, we obtain the wirelength (exact and minimum) of embedding complete multi-partite graphs into Cartesian product of paths and/or cycles, which include n-cube, n-dimensional mesh (grid), n-dimensional cylinder and ndimensional torus, etc., as the subfamilies.

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“…Lemma 1.1. [27] Let f : G → H be an embedding with |V (G)| = |V (H)|. Let S ⊆ E(H) be such that E(H) \ S has exactly two subgraphs H 1 and H 2 , and let…”

Section: E=xy∈e(h)mentioning

confidence: 99%

Embedding complete multi-partite graphs into Cartesian product of paths and cycles

Rajan

Shantrinal

Rajalaxmi

et al. 2021

EJGTA

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“…Lemma 1. (Modified Congestion Lemma) (See [32,36].) Let f be an embedding of an arbitrary graph G into H. Let S be an edge cut of H such that the removal of edges of S leaves H into 2 components H 1 and H 2 and let…”

Section: Preliminaries Settingmentioning

confidence: 99%

“…In this paper, we present an algorithm for finding the embedding of Complete multipartite graphs into cycle-of-ladders and prove its correctness using the Modified Congestion lemma [32,36] and Partition lemma [32].…”

Section: Introductionmentioning

confidence: 99%

Embedding of Complete Multipartite Graphs Into Cycle-of-Ladders

Liu¹,

Karthik²,

Kumar³

2020

Int. J. of Appl. Math.

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Graph embedding is the mapping of a topological structure (guest graph) into another topological structure (host graph) that preserves certain required topological properties and the graph embedding ability reflects how efficiently a parallel algorithm with a guest graph can be executed on a host graph [1] and the utilization of system resources in the host graph [2]. In this paper, we obtain exact wirelength of embedding complete multipartite graphs into cycle-of-ladders.

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“…In recent years, Manuel et al obtained a lower bound for dilation of an embedding using minimum wirelength and formulated the result as IPS Lemma [25], and in 2014 the same authors computed an improved bound without using wirelength and formulated the result as Dilation Lemma [26]. The same authors obtained a technique to compute the wirelength of an embedding using the Modified Congestion Lemma [27] in 2014. In this direction, we propose and prove the Edge Congestion Lemma to obtain a tight bound for congestion of an embedding.…”

Section: Tight Boundmentioning

confidence: 99%

A Tight Bound for Congestion of an Embedding

Manuel

Rajasingh

Rajan

et al. 2015

Algorithms and Discrete Applied Mathematics

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Abstract. Graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. Congestion is one of the main optimization objectives in global routing. In this paper, we introduce a technique to obtain a tight bound for congestion of an embedding. Moreover, we give algorithms to compute exact congestion of embedding the hypercubes into the cylinder and the torus and prove that the bound obtained is sharp.

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Minimum Linear Arrangement of Incomplete Hypercubes

Cited by 24 publications

References 0 publications

Embedding complete multi-partite graphs into Cartesian product of paths and cycles

Embedding complete multi-partite graphs into Cartesian product of paths and cycles

Embedding of Complete Multipartite Graphs Into Cycle-of-Ladders

A Tight Bound for Congestion of an Embedding

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